Resources would be distributed evenly to each token the system would automatically attempt to have each token have an equal piece of the total of that resource owned by your empire. (So with 7 tokens of iron distributed each token would get 1/7th of the total supply of iron resource in your empire)
This item means that there is storage. The system will try to automatically ensure that each token represents an equal level of stockpile. So if there are no resources being used anywhere then the new supplies will be distributed evenly and stockpiles everywhere will increase. If one place is using resources but nowhere else then the new resources will go to replenish the depleted stockpiles. If the stockpiles are being depleted faster than they can be replenished and get below a certain point (user controlled) then:
You can set automatic alerts when a certain token/city is not getting sufficiently supplied or when the global supply of a resource drops to a certain amount. (With certain options to fix it. More management options are only given as needed)
So then you have the option of say draining a nearby stockpile to replenish your stocks. Otherwise it is all handled behind the scenes. So everything is simple and automated until it's important and you need it not to be, then you get choices to manage resource flow.